scatteractionsfinder.cc

Go to the documentation of this file.

/*
 *
 *    Copyright (c) 2014-2019
 *      SMASH Team
 *
 *    GNU General Public License (GPLv3 or later)
 *
 */

#include "smash/scatteractionsfinder.h"

#include <algorithm>
#include <map>
#include <vector>

#include "smash/configuration.h"
#include "smash/constants.h"
#include "smash/crosssections.h"
#include "smash/cxx14compat.h"
#include "smash/decaymodes.h"
#include "smash/experimentparameters.h"
#include "smash/isoparticletype.h"
#include "smash/logging.h"
#include "smash/macros.h"
#include "smash/particles.h"
#include "smash/scatteraction.h"
#include "smash/scatteractionphoton.h"
#include "smash/stringfunctions.h"

namespace smash {
ScatterActionsFinder::ScatterActionsFinder(
    Configuration config, const ExperimentParameters& parameters,
    const std::vector<bool>& nucleon_has_interacted, int N_tot, int N_proj)
    : coll_crit_(config.take({"Collision_Term", "Collision_Criterion"},
                             CollisionCriterion::Geometric)),
      elastic_parameter_(
          config.take({"Collision_Term", "Elastic_Cross_Section"}, -1.)),
      testparticles_(parameters.testparticles),
      isotropic_(config.take({"Collision_Term", "Isotropic"}, false)),
      two_to_one_(parameters.two_to_one),
      incl_set_(parameters.included_2to2),
      low_snn_cut_(parameters.low_snn_cut),
      strings_switch_(parameters.strings_switch),
      use_AQM_(parameters.use_AQM),
      strings_with_probability_(parameters.strings_with_probability),
      nnbar_treatment_(parameters.nnbar_treatment),
      nucleon_has_interacted_(nucleon_has_interacted),
      N_tot_(N_tot),
      N_proj_(N_proj),
      string_formation_time_(config.take(
          {"Collision_Term", "String_Parameters", "Formation_Time"}, 1.)) {
  if (coll_crit_ == CollisionCriterion::Stochastic &&
      !(is_constant_elastic_isotropic())) {
    throw std::invalid_argument(
        "The stochastic collision criterion is only supported for elastic (and "
        "isotropic)\n2-to-2 reactions of one particle species. Change you "
        "config accordingly.");
  }
  if (is_constant_elastic_isotropic()) {
    const auto& log = logger<LogArea::FindScatter>();
    log.info("Constant elastic isotropic cross-section mode:", " using ",
             elastic_parameter_, " mb as maximal cross-section.");
  }
  if (strings_switch_) {
    auto subconfig = config["Collision_Term"]["String_Parameters"];
    string_process_interface_ = make_unique<StringProcess>(
        subconfig.take({"String_Tension"}, 1.0), string_formation_time_,
        subconfig.take({"Gluon_Beta"}, 0.5),
        subconfig.take({"Gluon_Pmin"}, 0.001),
        subconfig.take({"Quark_Alpha"}, 2.0),
        subconfig.take({"Quark_Beta"}, 7.0),
        subconfig.take({"Strange_Supp"}, 0.16),
        subconfig.take({"Diquark_Supp"}, 0.036),
        subconfig.take({"Sigma_Perp"}, 0.42),
        subconfig.take({"StringZ_A_Leading"}, 0.2),
        subconfig.take({"StringZ_B_Leading"}, 2.0),
        subconfig.take({"StringZ_A"}, 2.0), subconfig.take({"StringZ_B"}, 0.55),
        subconfig.take({"String_Sigma_T"}, 0.5),
        subconfig.take({"Form_Time_Factor"}, 1.0),
        subconfig.take({"Mass_Dependent_Formation_Times"}, false),
        subconfig.take({"Prob_proton_to_d_uu"}, 1. / 3.),
        subconfig.take({"Separate_Fragment_Baryon"}, true),
        subconfig.take({"Popcorn_Rate"}, 0.15));
  }
}

ActionPtr ScatterActionsFinder::check_collision(
    const ParticleData& data_a, const ParticleData& data_b, double dt,
    const std::vector<FourVector>& beam_momentum, const double cell_vol) const {
  const auto& log = logger<LogArea::FindScatter>();

  /* If the two particles
   * 1) belong to the two colliding nuclei
   * 2) are within the same nucleus
   * 3) both of them have never experienced any collisons,
   * then the collision between them are banned. */
  assert(data_a.id() >= 0);
  assert(data_b.id() >= 0);
  if (data_a.id() < N_tot_ && data_b.id() < N_tot_ &&
      ((data_a.id() < N_proj_ && data_b.id() < N_proj_) ||
       (data_a.id() >= N_proj_ && data_b.id() >= N_proj_)) &&
      !(nucleon_has_interacted_[data_a.id()] ||
        nucleon_has_interacted_[data_b.id()])) {
    return nullptr;
  }

  // Determine time of collision.
  const double time_until_collision =
      collision_time(data_a, data_b, dt, beam_momentum);

  // Check that collision happens in this timestep.
  if (time_until_collision < 0. || time_until_collision >= dt) {
    return nullptr;
  }

  // Create ScatterAction object.
  ScatterActionPtr act = make_unique<ScatterAction>(
      data_a, data_b, time_until_collision, isotropic_, string_formation_time_);

  if (strings_switch_) {
    act->set_string_interface(string_process_interface_.get());
  }

  if (coll_crit_ == CollisionCriterion::Stochastic) {
    // No grid or search in cell
    if (cell_vol < really_small) {
      return nullptr;
    }

    // Add various subprocesses.
    act->add_all_scatterings(elastic_parameter_, two_to_one_, incl_set_,
                             low_snn_cut_, strings_switch_, use_AQM_,
                             strings_with_probability_, nnbar_treatment_);

    const double xs = act->cross_section() * fm2_mb;

    // Relative velocity calculation, see e.g. \iref{Seifert:2017oyb}, eq. (5)
    const double m1 = act->incoming_particles()[0].effective_mass();
    const double m1_sqr = m1 * m1;
    const double m2 = act->incoming_particles()[1].effective_mass();
    const double m2_sqr = m2 * m2;
    const double e1 = act->incoming_particles()[0].momentum().x0();
    const double e2 = act->incoming_particles()[1].momentum().x0();
    const double m_s = act->mandelstam_s();
    const double lambda = (m_s - m1_sqr - m2_sqr) * (m_s - m1_sqr - m2_sqr) -
                          4. * m1_sqr * m2_sqr;
    const double v_rel = std::sqrt(lambda) / (2. * e1 * e2);

    // Collision probability, see e.g. \iref{Xu:2004mz}, eq. (11)
    const double p_22 = xs * v_rel * dt / (cell_vol * testparticles_);

    log.debug("Stochastic collison criterion parameters:\np_22 = ", p_22,
              ", xs = ", xs, ", v_rel = ", v_rel, ", dt = ", dt,
              ", cell_vol = ", cell_vol, ", testparticles = ", testparticles_);

    if (p_22 > 1.) {
      std::stringstream err;
      err << "Probability larger than 1 for stochastic rates. ( P = " << p_22
          << " )\nUse smaller timesteps.";
      throw std::runtime_error(err.str());
    }

    // probability criterion
    double random_no = random::uniform(0., 1.);
    if (random_no > p_22) {
      return nullptr;
    }

  } else if (coll_crit_ == CollisionCriterion::Geometric) {
    // just collided with this particle
    if (data_a.id_process() > 0 && data_a.id_process() == data_b.id_process()) {
      log.debug("Skipping collided particles at time ", data_a.position().x0(),
                " due to process ", data_a.id_process(), "\n    ", data_a,
                "\n<-> ", data_b);
      return nullptr;
    }

    const double distance_squared = act->transverse_distance_sqr();

    // Don't calculate cross section if the particles are very far apart.
    if (distance_squared >= max_transverse_distance_sqr(testparticles_)) {
      return nullptr;
    }

    // Add various subprocesses.
    act->add_all_scatterings(elastic_parameter_, two_to_one_, incl_set_,
                             low_snn_cut_, strings_switch_, use_AQM_,
                             strings_with_probability_, nnbar_treatment_);

    // Cross section for collision criterion
    double cross_section_criterion = act->cross_section() * fm2_mb * M_1_PI /
                                     static_cast<double>(testparticles_);

    // Take cross section scaling factors into account
    cross_section_criterion *= data_a.xsec_scaling_factor(time_until_collision);
    cross_section_criterion *= data_b.xsec_scaling_factor(time_until_collision);

    // distance criterion according to cross_section
    if (distance_squared >= cross_section_criterion) {
      return nullptr;
    }

    log.debug("particle distance squared: ", distance_squared, "\n    ", data_a,
              "\n<-> ", data_b);
  }

  // Using std::move here is redundant with newer compilers, but required for
  // supporting GCC 4.8. Once we drop this support, std::move should be removed.
  return std::move(act);
}

ActionList ScatterActionsFinder::find_actions_in_cell(
    const ParticleList& search_list, double dt, const double cell_vol,
    const std::vector<FourVector>& beam_momentum) const {
  std::vector<ActionPtr> actions;
  for (const ParticleData& p1 : search_list) {
    for (const ParticleData& p2 : search_list) {
      if (p1.id() < p2.id()) {
        // Check if a collision is possible.
        ActionPtr act = check_collision(p1, p2, dt, beam_momentum, cell_vol);
        if (act) {
          actions.push_back(std::move(act));
        }
      }
    }
  }
  return actions;
}

ActionList ScatterActionsFinder::find_actions_with_neighbors(
    const ParticleList& search_list, const ParticleList& neighbors_list,
    double dt, const std::vector<FourVector>& beam_momentum) const {
  std::vector<ActionPtr> actions;
  if (coll_crit_ == CollisionCriterion::Stochastic) {
    // Only search in cells
    return actions;
  }
  for (const ParticleData& p1 : search_list) {
    for (const ParticleData& p2 : neighbors_list) {
      assert(p1.id() != p2.id());
      // Check if a collision is possible.
      ActionPtr act = check_collision(p1, p2, dt, beam_momentum);
      if (act) {
        actions.push_back(std::move(act));
      }
    }
  }
  return actions;
}

ActionList ScatterActionsFinder::find_actions_with_surrounding_particles(
    const ParticleList& search_list, const Particles& surrounding_list,
    double dt, const std::vector<FourVector>& beam_momentum) const {
  std::vector<ActionPtr> actions;
  if (coll_crit_ == CollisionCriterion::Stochastic) {
    // Only search in cells
    return actions;
  }
  for (const ParticleData& p2 : surrounding_list) {
    /* don't look for collisions if the particle from the surrounding list is
     * also in the search list */
    auto result = std::find_if(
        search_list.begin(), search_list.end(),
        [&p2](const ParticleData& p) { return p.id() == p2.id(); });
    if (result != search_list.end()) {
      continue;
    }
    for (const ParticleData& p1 : search_list) {
      // Check if a collision is possible.
      ActionPtr act = check_collision(p1, p2, dt, beam_momentum);
      if (act) {
        actions.push_back(std::move(act));
      }
    }
  }
  return actions;
}

void ScatterActionsFinder::dump_reactions() const {
  constexpr double time = 0.0;

  const size_t N_isotypes = IsoParticleType::list_all().size();
  const size_t N_pairs = N_isotypes * (N_isotypes - 1) / 2;

  std::cout << N_isotypes << " iso-particle types." << std::endl;
  std::cout << "They can make " << N_pairs << " pairs." << std::endl;
  std::vector<double> momentum_scan_list = {0.1, 0.3, 0.5, 1.0,
                                            2.0, 3.0, 5.0, 10.0};
  for (const IsoParticleType& A_isotype : IsoParticleType::list_all()) {
    for (const IsoParticleType& B_isotype : IsoParticleType::list_all()) {
      if (&A_isotype > &B_isotype) {
        continue;
      }
      bool any_nonzero_cs = false;
      std::vector<std::string> r_list;
      for (const ParticleTypePtr A_type : A_isotype.get_states()) {
        for (const ParticleTypePtr B_type : B_isotype.get_states()) {
          if (A_type > B_type) {
            continue;
          }
          ParticleData A(*A_type), B(*B_type);
          for (auto mom : momentum_scan_list) {
            A.set_4momentum(A.pole_mass(), mom, 0.0, 0.0);
            B.set_4momentum(B.pole_mass(), -mom, 0.0, 0.0);
            ScatterActionPtr act = make_unique<ScatterAction>(
                A, B, time, isotropic_, string_formation_time_);
            if (strings_switch_) {
              act->set_string_interface(string_process_interface_.get());
            }
            act->add_all_scatterings(elastic_parameter_, two_to_one_, incl_set_,
                                     low_snn_cut_, strings_switch_, use_AQM_,
                                     strings_with_probability_,
                                     nnbar_treatment_);
            const double total_cs = act->cross_section();
            if (total_cs <= 0.0) {
              continue;
            }
            any_nonzero_cs = true;
            for (const auto& channel : act->collision_channels()) {
              const auto type = channel->get_type();
              std::string r;
              if (is_string_soft_process(type) ||
                  type == ProcessType::StringHard) {
                r = A_type->name() + B_type->name() + std::string(" → strings");
              } else {
                std::string r_type =
                    (type == ProcessType::Elastic)
                        ? std::string(" (el)")
                        : (channel->get_type() == ProcessType::TwoToTwo)
                              ? std::string(" (inel)")
                              : std::string(" (?)");
                r = A_type->name() + B_type->name() + std::string(" → ") +
                    channel->particle_types()[0]->name() +
                    channel->particle_types()[1]->name() + r_type;
              }
              isoclean(r);
              r_list.push_back(r);
            }
          }
        }
      }
      std::sort(r_list.begin(), r_list.end());
      r_list.erase(std::unique(r_list.begin(), r_list.end()), r_list.end());
      if (any_nonzero_cs) {
        for (auto r : r_list) {
          std::cout << r;
          if (r_list.back() != r) {
            std::cout << ", ";
          }
        }
        std::cout << std::endl;
      }
    }
  }
}

struct FinalStateCrossSection {
  std::string name_;

  double cross_section_;

  double mass_;

  FinalStateCrossSection(const std::string& name, double cross_section,
                         double mass)
      : name_(name), cross_section_(cross_section), mass_(mass) {}
};

namespace decaytree {

struct Node {
 public:
  std::string name_;

  double weight_;

  ParticleTypePtrList initial_particles_;

  ParticleTypePtrList final_particles_;

  ParticleTypePtrList state_;

  std::vector<Node> children_;

  Node(const Node&) = delete;
  Node(Node&&) = default;

  Node(const std::string& name, double weight,
       ParticleTypePtrList&& initial_particles,
       ParticleTypePtrList&& final_particles, ParticleTypePtrList&& state,
       std::vector<Node>&& children)
      : name_(name),
        weight_(weight),
        initial_particles_(std::move(initial_particles)),
        final_particles_(std::move(final_particles)),
        state_(std::move(state)),
        children_(std::move(children)) {}

  Node& add_action(const std::string& name, double weight,
                   ParticleTypePtrList&& initial_particles,
                   ParticleTypePtrList&& final_particles) {
    // Copy parent state and update it.
    ParticleTypePtrList state(state_);
    for (const auto& p : initial_particles) {
      state.erase(std::find(state.begin(), state.end(), p));
    }
    for (const auto& p : final_particles) {
      state.push_back(p);
    }
    // Sort the state to normalize the output.
    std::sort(state.begin(), state.end(),
              [](ParticleTypePtr a, ParticleTypePtr b) {
                return a->name() < b->name();
              });
    // Push new node to children.
    Node new_node(name, weight, std::move(initial_particles),
                  std::move(final_particles), std::move(state), {});
    children_.emplace_back(std::move(new_node));
    return children_.back();
  }

  void print() const { print_helper(0); }

  std::vector<FinalStateCrossSection> final_state_cross_sections() const {
    std::vector<FinalStateCrossSection> result;
    final_state_cross_sections_helper(0, result, "", 1.);
    return result;
  }

 private:
  void print_helper(uint64_t depth) const {
    for (uint64_t i = 0; i < depth; i++) {
      std::cout << " ";
    }
    std::cout << name_ << " " << weight_ << std::endl;
    for (const auto& child : children_) {
      child.print_helper(depth + 1);
    }
  }

  void final_state_cross_sections_helper(
      uint64_t depth, std::vector<FinalStateCrossSection>& result,
      const std::string& name, double weight,
      bool show_intermediate_states = false) const {
    // The first node corresponds to the total cross section and has to be
    // ignored. The second node corresponds to the partial cross section. All
    // further nodes correspond to branching ratios.
    if (depth > 0) {
      weight *= weight_;
    }

    std::string new_name;
    double mass = 0.;

    if (show_intermediate_states) {
      new_name = name;
      if (!new_name.empty()) {
        new_name += "->";
      }
      new_name += name_;
      new_name += "{";
    } else {
      new_name = "";
    }
    for (const auto& s : state_) {
      new_name += s->name();
      mass += s->mass();
    }
    if (show_intermediate_states) {
      new_name += "}";
    }

    if (children_.empty()) {
      result.emplace_back(FinalStateCrossSection(new_name, weight, mass));
      return;
    }
    for (const auto& child : children_) {
      child.final_state_cross_sections_helper(depth + 1, result, new_name,
                                              weight, show_intermediate_states);
    }
  }
};

static std::string make_decay_name(const std::string& res_name,
                                   const DecayBranchPtr& decay,
                                   ParticleTypePtrList& final_state) {
  std::stringstream name;
  name << "[" << res_name << "->";
  for (const auto& p : decay->particle_types()) {
    name << p->name();
    final_state.push_back(p);
  }
  name << "]";
  return name.str();
}

static void add_decays(Node& node, double sqrts) {
  // If there is more than one unstable particle in the current state, then
  // there will be redundant paths in the decay tree, corresponding to
  // reorderings of the decays. To avoid double counting, we normalize by the
  // number of possible decay orderings. Normalizing by the number of unstable
  // particles recursively corresponds to normalizing by the factorial that
  // gives the number of reorderings.
  //
  // Ideally, the redundant paths should never be added to the decay tree, but
  // we never have more than two redundant paths, so it probably does not matter
  // much.
  uint32_t n_unstable = 0;
  double sqrts_minus_masses = sqrts;
  for (const ParticleTypePtr ptype : node.state_) {
    if (!ptype->is_stable()) {
      n_unstable += 1;
    }
    sqrts_minus_masses -= ptype->mass();
  }
  const double norm =
      n_unstable != 0 ? 1. / static_cast<double>(n_unstable) : 1.;

  for (const ParticleTypePtr ptype : node.state_) {
    if (!ptype->is_stable()) {
      const double sqrts_decay = sqrts_minus_masses + ptype->mass();
      bool can_decay = false;
      for (const auto& decay : ptype->decay_modes().decay_mode_list()) {
        // Make sure to skip kinematically impossible decays.
        // In principle, we would have to integrate over the mass of the
        // resonance, but as an approximation we just assume it at its pole.
        double final_state_mass = 0.;
        for (const auto& p : decay->particle_types()) {
          final_state_mass += p->mass();
        }
        if (final_state_mass > sqrts_decay) {
          continue;
        }
        can_decay = true;

        ParticleTypePtrList parts;
        const auto name = make_decay_name(ptype->name(), decay, parts);
        auto& new_node = node.add_action(name, norm * decay->weight(), {ptype},
                                         std::move(parts));
        add_decays(new_node, sqrts_decay);
      }
      if (!can_decay) {
        // Remove final-state cross sections with resonances that cannot
        // decay due to our "mass = pole mass" approximation.
        node.weight_ = 0;
        return;
      }
    }
  }
}

}  // namespace decaytree

static void deduplicate(std::vector<FinalStateCrossSection>& final_state_xs) {
  std::sort(final_state_xs.begin(), final_state_xs.end(),
            [](const FinalStateCrossSection& a,
               const FinalStateCrossSection& b) { return a.name_ < b.name_; });
  auto current = final_state_xs.begin();
  while (current != final_state_xs.end()) {
    auto adjacent = std::adjacent_find(
        current, final_state_xs.end(),
        [](const FinalStateCrossSection& a, const FinalStateCrossSection& b) {
          return a.name_ == b.name_;
        });
    current = adjacent;
    if (adjacent != final_state_xs.end()) {
      adjacent->cross_section_ += (adjacent + 1)->cross_section_;
      final_state_xs.erase(adjacent + 1);
    }
  }
}

void ScatterActionsFinder::dump_cross_sections(
    const ParticleType& a, const ParticleType& b, double m_a, double m_b,
    bool final_state, std::vector<double>& plab) const {
  typedef std::vector<std::pair<double, double>> xs_saver;
  std::map<std::string, xs_saver> xs_dump;
  std::map<std::string, double> outgoing_total_mass;

  ParticleData a_data(a), b_data(b);
  int n_momentum_points = 200;
  constexpr double momentum_step = 0.02;
  /*
  // Round to output precision.
  for (auto& p : plab) {
    p = std::floor((p * 100000) + 0.5) / 100000;
  }
  */
  if (plab.size() > 0) {
    n_momentum_points = plab.size();
    // Remove duplicates.
    std::sort(plab.begin(), plab.end());
    plab.erase(std::unique(plab.begin(), plab.end()), plab.end());
  }
  for (int i = 0; i < n_momentum_points; i++) {
    double momentum;
    if (plab.size() > 0) {
      momentum = pCM_from_s(s_from_plab(plab.at(i), m_a, m_b), m_a, m_b);
    } else {
      momentum = momentum_step * (i + 1);
    }
    a_data.set_4momentum(m_a, momentum, 0.0, 0.0);
    b_data.set_4momentum(m_b, -momentum, 0.0, 0.0);
    const double sqrts = (a_data.momentum() + b_data.momentum()).abs();
    const ParticleList incoming = {a_data, b_data};
    ScatterActionPtr act = make_unique<ScatterAction>(
        a_data, b_data, 0., isotropic_, string_formation_time_);
    if (strings_switch_) {
      act->set_string_interface(string_process_interface_.get());
    }
    act->add_all_scatterings(elastic_parameter_, two_to_one_, incl_set_,
                             low_snn_cut_, strings_switch_, use_AQM_,
                             strings_with_probability_, nnbar_treatment_);
    decaytree::Node tree(a.name() + b.name(), act->cross_section(), {&a, &b},
                         {&a, &b}, {&a, &b}, {});
    const CollisionBranchList& processes = act->collision_channels();
    for (const auto& process : processes) {
      const double xs = process->weight();
      if (xs <= 0.0) {
        continue;
      }
      if (!final_state) {
        std::stringstream process_description_stream;
        process_description_stream << *process;
        const std::string& description = process_description_stream.str();
        double m_tot = 0.0;
        for (const auto& ptype : process->particle_types()) {
          m_tot += ptype->mass();
        }
        outgoing_total_mass[description] = m_tot;
        if (!xs_dump[description].empty() &&
            std::abs(xs_dump[description].back().first - sqrts) <
                really_small) {
          xs_dump[description].back().second += xs;
        } else {
          xs_dump[description].push_back(std::make_pair(sqrts, xs));
        }
      } else {
        std::stringstream process_description_stream;
        process_description_stream << *process;
        const std::string& description = process_description_stream.str();
        ParticleTypePtrList initial_particles = {&a, &b};
        ParticleTypePtrList final_particles = process->particle_types();
        auto& process_node =
            tree.add_action(description, xs, std::move(initial_particles),
                            std::move(final_particles));
        decaytree::add_decays(process_node, sqrts);
      }
    }
    xs_dump["total"].push_back(std::make_pair(sqrts, act->cross_section()));
    // Total cross-section should be the first in the list -> negative mass
    outgoing_total_mass["total"] = -1.0;
    if (final_state) {
      // tree.print();
      auto final_state_xs = tree.final_state_cross_sections();
      deduplicate(final_state_xs);
      for (const auto& p : final_state_xs) {
        // Don't print empty columns.
        //
        // FIXME(steinberg): The better fix would be to not have them in the
        // first place.
        if (p.name_ == "") {
          continue;
        }
        outgoing_total_mass[p.name_] = p.mass_;
        xs_dump[p.name_].push_back(std::make_pair(sqrts, p.cross_section_));
      }
    }
  }
  // Get rid of cross sections that are zero.
  // (This only happens if their is a resonance in the final state that cannot
  // decay with our simplified assumptions.)
  for (auto it = begin(xs_dump); it != end(xs_dump);) {
    // Sum cross section over all energies.
    const xs_saver& xs = (*it).second;
    double sum = 0;
    for (const auto& p : xs) {
      sum += p.second;
    }
    if (sum == 0.) {
      it = xs_dump.erase(it);
    } else {
      ++it;
    }
  }

  // Nice ordering of channels by summed pole mass of products
  std::vector<std::string> all_channels;
  for (const auto channel : xs_dump) {
    all_channels.push_back(channel.first);
  }
  std::sort(all_channels.begin(), all_channels.end(),
            [&](const std::string& str_a, const std::string& str_b) {
              return outgoing_total_mass[str_a] < outgoing_total_mass[str_b];
            });

  // Print header
  std::cout << "# Dumping partial " << a.name() << b.name()
            << " cross-sections in mb, energies in GeV" << std::endl;
  std::cout << "   sqrt_s";
  // Align everything to 16 unicode characters.
  // This should be enough for the longest channel name (7 final-state
  // particles).
  for (const auto channel : all_channels) {
    std::cout << utf8::fill_left(channel, 16, ' ');
  }
  std::cout << std::endl;

  // Print out all partial cross-sections in mb
  for (int i = 0; i < n_momentum_points; i++) {
    double momentum;
    if (plab.size() > 0) {
      momentum = pCM_from_s(s_from_plab(plab.at(i), m_a, m_b), m_a, m_b);
    } else {
      momentum = momentum_step * (i + 1);
    }
    a_data.set_4momentum(m_a, momentum, 0.0, 0.0);
    b_data.set_4momentum(m_b, -momentum, 0.0, 0.0);
    const double sqrts = (a_data.momentum() + b_data.momentum()).abs();
    std::printf("%9.6f", sqrts);
    for (const auto channel : all_channels) {
      const xs_saver energy_and_xs = xs_dump[channel];
      size_t j = 0;
      for (; j < energy_and_xs.size() && energy_and_xs[j].first < sqrts; j++) {
      }
      double xs = 0.0;
      if (j < energy_and_xs.size() &&
          std::abs(energy_and_xs[j].first - sqrts) < really_small) {
        xs = energy_and_xs[j].second;
      }
      std::printf("%16.6f", xs);  // Same alignment as in the header.
    }
    std::printf("\n");
  }
}

}  // namespace smash